Role of vertex corrections in the matrix formulation of the random phase approximation for the multiorbital Hubbard model

TL;DR

This paper investigates the role of vertex corrections in the matrix formulation of the RPA for multiorbital Hubbard models, clarifying their impact on superconducting pairing interactions.

Contribution

It reveals the presence of vertex correction terms in the matrix RPA formulation and analyzes their diagrammatic structure and significance.

Findings

Vertex corrections naturally arise in the matrix RPA formulation.

These corrections have the diagrammatic structure of vertex correction diagrams.

The study clarifies the relationship between matrix RPA and Feynman diagrams.

Abstract

In the framework of a multiorbital Hubbard model description of superconductivity, a matrix formulation of the superconducting pairing interaction that has been widely used is designed to treat spin, charge and orbital fluctuations within a random phase approximation (RPA). In terms of Feynman diagrams, this takes into account particle-hole ladder and bubble contributions as expected. It turns out, however, that this matrix formulation also generates additional terms which have the diagrammatic structure of vertex corrections. Here we examine these terms and discuss the relationship between the matrix-RPA superconducting pairing interaction and the Feynman diagrams that it sums.